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Visual/Spatial Recognition Skills
1.a.
Stage 1
MLSN 2008-2009
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1. b.
Stage 2
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1.c.
Stage 3
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2.a.
Stage 1
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2.b.
Stage 2
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2.c.
Stage 3
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3.a.
Stage 1
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3.b.
Stage 2
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3.c.
Stage 3
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For each sequence of geometric patterns given above, have students work in pairs
and do as many of the following steps as is developmentally appropriate.
I. Show students the pattern 1, Stage 1 above using an overhead or multimedia
projector. After a few seconds, remove the slide and have the students draw or
build it with cubes.
II. Have the students leave the just built Stage 1in place. Show students the Stage
2 above using an overhead or multimedia projector. After a few seconds,
remove the slide and have the students draw or use cubes to build Stage 2.
III. Do the same for Stage 3.
IV. Without showing the students any diagram, have students draw or build what
they believe would be Stage 4 and Stage 5.
V. Perform a teacher check and ask each pair of students to think about how they
know they are correct. Have students fill in the tables provided for each
pattern.
VI. Work through Pattern 1 with the whole group of students (See teacher notes at
the end). When you have completely finished Pattern 1 with the whole group
of students, have the pairs of students work through sections I through V for
patterns 2 and 3.
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Pattern 1
STAGE
Number
3
10
57
n
(any
STAGE
number)
Write a rule for the total
number of squares in each
STAGE
-stage no. plus 1 plus 1
extra
------------------------------Stage no.plus 2
------------------------------ 2 plus stage no.
-Stage no.plus 1 plus 1
extra
-----------------------------Stage no.plus 2
-----------------------------2 plus stage no.
-Stage no.plus 1 plus 1
extra
-----------------------------Stage no.plus 2
-----------------------------2 plus stage no.
Symbolic Rule for
the total squares in
each STAGE
Total numbers of
squares in each
STAGE
(3 + 1) + 1
--------------------3+2
--------------------2+3
5
--------------5
---------------5
12
(10 + 1) + 1
-------------------10 + 2
------------------2 + 10
---------------12
---------------12
(57+1) + 1
---------------------57 + 2
--------------------2 + 57
59
-------------------59
-------------------59
- Stage no. plus 1 plus 1
(n + 1) + 1
n+2
------------------------------- Stage no.plus 2
------------------------------ 2 + stage no.
-------------------n+2
-------------------2+n
------------------n+2
------------------n+2
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Pattern 2
STAGE
Number
Write a rule for the total
number of squares in each
STAGE
Symbolic Rule for
the total squares in
each STAGE
Total numbers of
squares in each
STAGE
3
10
57
n
(any
STAGE
number)
MLSN 2008-2009
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Pattern 3
STAGE
Number
Write a rule for the total
number of squares in each
STAGE
Symbolic Rule for
the total squares in
each STAGE
Total numbers of
squares in each
STAGE
3
10
57
n
(any
STAGE
number)
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Pattern __
STAGE
Number
Write a rule for the total
number of squares in each
STAGE
Symbolic Rule for
the total squares in
each STAGE
Total numbers of
squares in each
STAGE
3
10
57
n
(any
STAGE
number)
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Additional TEACHER NOTES
In doing the activity with students, work through Pattern 1 with the whole group of
students. On the printed example, there are three different approaches students
may take as they ‘see’ the number of squares in each stage in each pattern. Even
for pattern 1, ask if any students saw the number of squares in each stage
differently and record any additional ones.
Instead of filling in the provided chart, you may just want to use the following
questions after students have built or drawn the first five stages for any pattern:
1. How many different patterns can you see in this sequence of stages?
How do you draw the next stage?
How do you build or draw the 10th stage?
How would you build or draw the 57th stage?
How would you tell someone how to draw any stage at all?
How would you restate your description of how to build or draw any stage if
that stage is called the nth stage?
2. If you have 35 squares or cubes to use, what is the largest stage of the pattern
you could build? Would you have any squares (or cubes) left over?
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3. How many squares (or cubes) does it take to build the 10th , the 57th or the 100th
stage?
4. How many squares (or cubes) does it take to make the nth stage?
Seeing a pattern is a necessary first step in pattern exploration, and simple growing
patterns are explicit, visual and easy to see. Using number patterns as 5, 8, 11, 14,
…are interesting, but they are less useful in the initial work of viewing a pattern
because they are less useful in the initial work of viewing a pattern because they
are less visual and do not give rise to a multiplicity of “seeing”.
Some additional patterns are given below.
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4.
Stage 1
Stage 2
Stage 3
5.
Stage 1
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Stage 2
Stage 3
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